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Simplifying (2a + 4)(4a + 7) = 0 Reorder the terms: (4 + 2a)(4a + 7) = 0 Reorder the terms: (4 + 2a)(7 + 4a) = 0 Multiply (4 + 2a) * (7 + 4a) (4(7 + 4a) + 2a * (7 + 4a)) = 0 ((7 * 4 + 4a * 4) + 2a * (7 + 4a)) = 0 ((28 + 16a) + 2a * (7 + 4a)) = 0 (28 + 16a + (7 * 2a + 4a * 2a)) = 0 (28 + 16a + (14a + 8a2)) = 0 Combine like terms: 16a + 14a = 30a (28 + 30a + 8a2) = 0 Solving 28 + 30a + 8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 15a + 4a2) = 0 Factor a trinomial. 2((2 + a)(7 + 4a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2Subproblem 2
Set the factor '(7 + 4a)' equal to zero and attempt to solve: Simplifying 7 + 4a = 0 Solving 7 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4a = 0 + -7 4a = 0 + -7 Combine like terms: 0 + -7 = -7 4a = -7 Divide each side by '4'. a = -1.75 Simplifying a = -1.75Solution
a = {-2, -1.75}
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